"I threw some compost around the base" STOP! That's asking for fungal infection in the trunk. Mulch the entire root area (out a couple of feet past the branch area) with 4-5 inches of compost or something, but keep the mulch 4-6 inches away from the base of the tree.

"and am watering it every day." STOP! Water it DEEPLY once a week. Frequent shallow watering lures the roots up into the top layer of soil and makes the tree more suceptible to drought and a brief lapse in watering. Deep watering gets the roots down into the lower layers where they can stay moist.

"Should I wait until this season has finished to see how far up the buds go before cutting back what appear to be all the dead branches." Yes. It may surprise you.